Why are there 360º in a circle¿
The Babylonians are to blame.
(The Babylonians had some fondness for the number 60, by the way, counting for 1 hour = 60 minutes of 60 seconds each. Since 360 = 6*60, this could come in as well)
It’s also nice because there are 365 days in a year, so the Earth moves approximately one degree around the Sun each day. Actually, they would have regarded that as the Sun moving one degree relative to the stars, but it works out the same.
So why not use 365 degrees in a circle and be done with it? Because 360 is a much nicer number. It’s divisible by 2, 3, 4, 5, 6, 8, and a bunch of other numbers. Which is nice if you’re trying to, say, cut a pie into equal-sized pieces.